Learning Top-Down Tree Transducers with Regular Domain Inspection

Proceedings of The 13th International Conference on Grammatical Inference, PMLR 57:54-65, 2017.

Abstract

We study the problem of how to learn tree transformations on a given regular tree domain from a finite sample of input-output examples. We assume that the target tree transformation can be defined by a deterministic top-down tree transducer with regular domain inspection (DTOPIreg). An RPNI style learning algorithm that solves this problem in polynomial time and with polynomially many examples was presented at Pods’2010, but restricted to the case of path-closed regular domains. In this paper, we show that this restriction can be removed. For this, we present a new normal form for DTOPIreg by extending the Myhill-Nerode theorem for DTOP to regular domain inspections in a nontrivial manner. The RPNI style learning algorithm can also be lifted but becomes more involved too.

Related Material

@InProceedings{pmlr-v57-boiret16,
title = {Learning Top-Down Tree Transducers with Regular Domain Inspection},
author = {Adrien Boiret and Aurélien Lemay and Joachim Niehren},
booktitle = {Proceedings of The 13th International Conference on Grammatical Inference},
pages = {54--65},
year = {2017},
editor = {Sicco Verwer and Menno van Zaanen and Rick Smetsers},
volume = {57},
series = {Proceedings of Machine Learning Research},
address = {Delft, The Netherlands},
month = {05--07 Oct},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v57/boiret16.pdf},
url = {http://proceedings.mlr.press/v57/boiret16.html},
abstract = {We study the problem of how to learn tree transformations on a given regular tree domain from a finite sample of input-output examples. We assume that the target tree transformation can be defined by a deterministic top-down tree transducer with regular domain inspection (DTOPIreg). An RPNI style learning algorithm that solves this problem in polynomial time and with polynomially many examples was presented at Pods’2010, but restricted to the case of path-closed regular domains. In this paper, we show that this restriction can be removed. For this, we present a new normal form for DTOPIreg by extending the Myhill-Nerode theorem for DTOP to regular domain inspections in a nontrivial manner. The RPNI style learning algorithm can also be lifted but becomes more involved too.}
}

%0 Conference Paper
%T Learning Top-Down Tree Transducers with Regular Domain Inspection
%A Adrien Boiret
%A Aurélien Lemay
%A Joachim Niehren
%B Proceedings of The 13th International Conference on Grammatical Inference
%C Proceedings of Machine Learning Research
%D 2017
%E Sicco Verwer
%E Menno van Zaanen
%E Rick Smetsers
%F pmlr-v57-boiret16
%I PMLR
%J Proceedings of Machine Learning Research
%P 54--65
%U http://proceedings.mlr.press
%V 57
%W PMLR
%X We study the problem of how to learn tree transformations on a given regular tree domain from a finite sample of input-output examples. We assume that the target tree transformation can be defined by a deterministic top-down tree transducer with regular domain inspection (DTOPIreg). An RPNI style learning algorithm that solves this problem in polynomial time and with polynomially many examples was presented at Pods’2010, but restricted to the case of path-closed regular domains. In this paper, we show that this restriction can be removed. For this, we present a new normal form for DTOPIreg by extending the Myhill-Nerode theorem for DTOP to regular domain inspections in a nontrivial manner. The RPNI style learning algorithm can also be lifted but becomes more involved too.

TY - CPAPER
TI - Learning Top-Down Tree Transducers with Regular Domain Inspection
AU - Adrien Boiret
AU - Aurélien Lemay
AU - Joachim Niehren
BT - Proceedings of The 13th International Conference on Grammatical Inference
PY - 2017/01/16
DA - 2017/01/16
ED - Sicco Verwer
ED - Menno van Zaanen
ED - Rick Smetsers
ID - pmlr-v57-boiret16
PB - PMLR
SP - 54
DP - PMLR
EP - 65
L1 - http://proceedings.mlr.press/v57/boiret16.pdf
UR - http://proceedings.mlr.press/v57/boiret16.html
AB - We study the problem of how to learn tree transformations on a given regular tree domain from a finite sample of input-output examples. We assume that the target tree transformation can be defined by a deterministic top-down tree transducer with regular domain inspection (DTOPIreg). An RPNI style learning algorithm that solves this problem in polynomial time and with polynomially many examples was presented at Pods’2010, but restricted to the case of path-closed regular domains. In this paper, we show that this restriction can be removed. For this, we present a new normal form for DTOPIreg by extending the Myhill-Nerode theorem for DTOP to regular domain inspections in a nontrivial manner. The RPNI style learning algorithm can also be lifted but becomes more involved too.
ER -